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Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels. ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

A graph in which each graph edge is replaced by a directed graph edge, also called a digraph. A directed graph having no multiple edges or loops (corresponding to a binary ...

A letter of the alphabet drawn with doubled vertical strokes is called doublestruck, or sometimes blackboard bold (because doublestruck characters provide a means of ...

An L-algebraic number is a number theta in (0,1) which satisfies sum_(k=0)^nc_kL(theta^k)=0, (1) where L(x) is the Rogers L-function and c_k are integers not all equal to 0 ...

On a Riemannian manifold M, there is a canonical connection called the Levi-Civita connection (pronounced lē-vē shi-vit-e), sometimes also known as the Riemannian connection ...

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...

A linear transformation between two vector spaces V and W is a map T:V->W such that the following hold: 1. T(v_1+v_2)=T(v_1)+T(v_2) for any vectors v_1 and v_2 in V, and 2. ...

The minimal polynomial of a matrix A is the monic polynomial in A of smallest degree n such that p(A)=sum_(i=0)^nc_iA^i=0. (1) The minimal polynomial divides any polynomial q ...

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. ...